## Yin Tat Lee (Univ. Washington)Oct 16, 2017. ## Title and Abstract
Kannan-Lovasz-Simonovitz (KLS) conjecture asserts that the isoperimetric constant of any isotropic convex set is uniformly bounded below. It turns out that this conjecture implies several well-known conjectures from multiple fields: (Convex Geometry) Each unit-volume convex set contains a constant area cross section. (Information Theory) Each isotropic logconcave distribution has O(d) KL distance to standard Gaussian distribution. (Statistics) A random marginal of a convex set is approximately a Gaussian distribution with 1/sqrt(d) error in total variation distance. (Measure Theory) Any function with Lipschitz constant 1 on an isotropic logconcave distribution is concentrated to its median by O(1). In this talk, we will discuss the latest development on the KLS conjecture. Joint work with Santosh Vempala. ## BioYin Tat Lee is an assistant professor in the Paul G. Allen School of Computer Science & Engineering at the University of Washington. He received his PhD from MIT in 2016. His research interests are primarily in algorithms and they span a wide range of topics such as convex optimization, convex geometry, spectral graph theory, and online algorithms |